BI-Axial Gegenbauer Functions of the 2nd Kind

Bi-axially symmetric monogenic generating functions on R(p divided by q) have been used recently to define generalisations of Gegenbauer polynomials. These polynomials are orthogonal on the unit ball in R(p). Generalised Cauchy transforms of these polynomials are used to define corresponding bi-axial Gegenbauer functions of the second kind. It is demonstrated that these functions of the second kind satisfy second order differential equations related to those satisfied by the corresponding bi-axial Gegenbauer polynomials. (C) 1995 Academic Press, Inc.